Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

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        <div xml:id="echoid-div356" type="section" level="1" n="128">
          <pb o="172" file="0248" n="274" rhead="CHRISTIANI HUGENII"/>
          <note position="left" xml:space="preserve">
            <emph style="sc">De centro</emph>
            <lb/>
            <emph style="sc">OSCILLA-</emph>
            <lb/>
            <emph style="sc">TIONIS</emph>
          .</note>
        </div>
        <div xml:id="echoid-div360" type="section" level="1" n="129">
          <head xml:id="echoid-head155" xml:space="preserve">PROPOSITIO XXIII.</head>
          <p style="it">
            <s xml:id="echoid-s3903" xml:space="preserve">HOrologiorum motum temperare, addito ponde-
              <lb/>
            re exiguo ſecundario, quod ſuper virga pen-
              <lb/>
            duli, certa ratione diviſa, ſurſum deorſumque
              <lb/>
            moveri poſſit.</s>
            <s xml:id="echoid-s3904" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3905" xml:space="preserve">Ut hoc expediamus, primo penduli ipſius, ex virga gra-
              <lb/>
              <note position="left" xlink:label="note-0248-02" xlink:href="note-0248-02a" xml:space="preserve">TAB. XXVII.
                <lb/>
              Fig. 3.</note>
            vitate prædita, & </s>
            <s xml:id="echoid-s3906" xml:space="preserve">appenſo parte ima pondere, compoſiti,
              <lb/>
            centrum oſcillationis inveniendum eſt.</s>
            <s xml:id="echoid-s3907" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3908" xml:space="preserve">Sit virga, cum appenſo pondere, A C, cujus longitudo
              <lb/>
            dicatur a. </s>
            <s xml:id="echoid-s3909" xml:space="preserve">Intelligantur autem, tum virga ipſa, tum pondus
              <lb/>
            appenſum C, in particulas minimas æquales diviſa, earum-
              <lb/>
            que particularum virga habeat numerum b, pondus vero C
              <lb/>
            numerum c, ponendo nempe b ad c, ſicut gravitas virgæ ad
              <lb/>
            gravitatem appenſi ponderis. </s>
            <s xml:id="echoid-s3910" xml:space="preserve">Longitudo igitur penduli ſim-
              <lb/>
            plicis, dato iſochroni, habebitur, ſi ſumma quadratorum à
              <lb/>
            diſtantiis particularum omnium à puncto ſuſpenſionis A, di-
              <lb/>
              <note symbol="*" position="left" xlink:label="note-0248-03" xlink:href="note-0248-03a" xml:space="preserve">Prop. 6.
                <lb/>
              huj. in fine.</note>
            vidatur per ſummam earundem diſtantiarum . </s>
            <s xml:id="echoid-s3911" xml:space="preserve">Secetur A C bifariam in M; </s>
            <s xml:id="echoid-s3912" xml:space="preserve">tum vero in T, ut A T ſit dupla T C. </s>
            <s xml:id="echoid-s3913" xml:space="preserve">Quia
              <lb/>
            ergo M eſt centrum gravitatis lineæ A C, & </s>
            <s xml:id="echoid-s3914" xml:space="preserve">A T ſubcen-
              <lb/>
            trica cunei ſuper ipſa abſciſſi plano per A D, perpendicu-
              <lb/>
            larem ad A C; </s>
            <s xml:id="echoid-s3915" xml:space="preserve">qui cuneus hîc revera triangulum eſt; </s>
            <s xml:id="echoid-s3916" xml:space="preserve">erit ſum-
              <lb/>
            ma quadratorum, à diſtantiis particularum virgæ à puncto
              <lb/>
            A, æqualis rectangulo A M T, una cum quadrato A M;
              <lb/>
            </s>
            <s xml:id="echoid-s3917" xml:space="preserve">hoc eſt, rectangulo T A M, multiplici ſecundum numerum
              <lb/>
            particularum b; </s>
            <s xml:id="echoid-s3918" xml:space="preserve">hoc eſt, {1/3} a a b; </s>
            <s xml:id="echoid-s3919" xml:space="preserve">quia M A eſt {1/2} a, & </s>
            <s xml:id="echoid-s3920" xml:space="preserve">T A
              <lb/>
            {2/3} a, ac proinde rectangulum T A M = {1/3} a a. </s>
            <s xml:id="echoid-s3921" xml:space="preserve">Summa vero
              <lb/>
            quadratorum, à diſtantiis particularum ponderis C ab eo-
              <lb/>
            dem puncto A, æquabitur quadrato A C, multiplici ſecun-
              <lb/>
            dum numerum particularum ipſius ponderis; </s>
            <s xml:id="echoid-s3922" xml:space="preserve">hoc eſt, a a c. </s>
            <s xml:id="echoid-s3923" xml:space="preserve">
              <lb/>
            Adeoque ſumma quadratorum omnium, tam à diſtantiis par-
              <lb/>
            ticularum virgæ, quam ponderis C, erit {1/3} a a b + a a c.</s>
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            <s xml:id="echoid-s3925" xml:space="preserve">Porro, diſtantiæ omnes particularum virgæ A C à pun-
              <lb/>
            cto A, æquantur {1/2} b a; </s>
            <s xml:id="echoid-s3926" xml:space="preserve">longitudini ſcilicet virgæ ipſius, </s>
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